Hybrid Energy Storage System

• HESS is an engineered integration of multiple storage technologies that leverages complementary strengths to satisfy both short- and long-term power needs.
• The system utilizes detailed mathematical models and multi-objective optimization—incorporating cost, degradation, and control tuning—to achieve optimal sizing and operation.
• Real-world applications in microgrids, EVs, and smart networks demonstrate cost savings, enhanced reliability, and adaptability through advanced data-driven and control strategies.

A Hybrid Energy Storage System (HESS) is an engineered combination of two or more distinct energy storage technologies, often equipped with advanced control and energy management strategies, to jointly satisfy the power and energy demands of applications whose charging/discharging requirements cannot be adequately met by a single storage technology. HESS architectures are foundational in renewable microgrids, electric vehicles, smart energy networks, and large-scale grid applications for cost-optimal, resilient, and lifecycle-aware storage utilization. The theoretical and practical design of HESSs is governed by detailed models that reflect the underlying storage physics, degradation phenomena, and techno-economics, as well as by numerical optimization methodologies for optimal sizing, control, and operation.

1. Core Principles and System Classification

A HESS is designed to exploit the complementary strengths of different storage technologies. Common pairings include lithium-ion batteries (LIB) with supercapacitors (SC), LIB with vanadium redox flow batteries (VRFB), LIB or conventional batteries with hydrogen storage (via electrolyzers and fuel cells), or batteries with flywheels. Architecturally, HESSs may be categorized by the timescale of the fluctuations each storage device is optimized to serve:

• Short timescale/high power: SCs, flywheels, or LIBs sized for high C-rate deliver fast response for peak-shaving, inertia emulation, or load transients.
• Long timescale/high energy: Flow batteries, LIBs with large energy capacity, or hydrogen systems carry bulk energy over hours to days.

In grid and microgrid contexts, application-specific sizing and power split rules are derived based on multi-timescale analysis of the load profile using metrics such as mean and 90th-percentile load, peak count rates, and transition rates. A data-driven approach can then partition the load into zones best served by each technology class (Zugschwert et al., 2022, Foles et al., 2023).

2. Mathematical Modeling and Physical Constraints

The governing equations for HESS sizing and control include detailed cost, degradation, and operational models for each storage layer:

Battery and Flow Battery Models

• LIB: Capital cost is modeled as $C_{\rm LIB}^E = c_e^{\rm LIB} E_{\rm LIB}$ (energy, \$285/kWh baseline),$$C_{\rm LIB}^P = c_p^{\rm LIB} P_{\rm LIB}$$(\$306/kW), with cycle life $N_{\rm cycle,\,LIB,max}=3\,500$ and calendar life $T_{\rm cal,\,LIB}=10$ yr. Premature failure is modeled via annualized cycles, $n_{\rm cycle,\,yr}$, with replacement triggered at $$T_{\rm real} = \min(T_{\rm cal}, N_{\rm cycle,\,max}/n_{\rm cycle,\,yr})$$.
• VRFB: Module cost follows $C_{\rm mod}^{\rm VRFB}(E/P) = A\exp(-B\,E/P) - D$, capturing nonlinearities at long durations. Additional costs for electrolyte, commissioning, and power electronics are included, with $T_{\rm cal,\,VRFB}=15$ yr and $N_{\rm cycle,\,VRFB,max}=10\,000$ (Cohen et al., 2021, Foles et al., 2023).

Supercapacitors and Flywheels

• SC: Modeled by $C_{\rm sc}$ series capacitance and $R_{\rm sc}$, with very high power density, negligible cycle aging, but low energy density.
• FESS: Modeled via $C_{\rm FESS}$ (rotational inertia), with key constraints on ramp rate and round-trip efficiency.

Hydrogen Storage

• Hydrogen path: Involves electrolyzers (efficiency $\eta_{\rm EL}$), storage tanks of theoretical capacity $V_{\rm cav}$ (for geologic scale or pressure vessels for smaller scales), and fuel cells (efficiency $\eta_{\rm FC}$). End-to-end round-trip efficiency is typically $30–45\%$ (Zhao et al., 2022, Diabate et al., 2 Jun 2024).

Hybrid System Constraints

• Power balance: $$\sum_{i}{P_{i,\rm out}} + P_{\rm RES}(t) = P_{\rm load}(t) + \text{losses}$$, where $i$ runs over all storage devices.
• State trajectories: $0 \leq E_{\rm dev}(t) \leq E_{\rm max}$, $$P_{\rm dev,\min} \leq P_{\rm dev}(t) \leq P_{\rm dev,\max}$$, $$\text{SOC}_{\min} \leq \text{SOC}(t) \leq \text{SOC}_{\max}$$—where each constraint is chemistry- and system-specific.
• Degradation: Capacity fade per cycle, $Q_{\rm deg}$, follows empirical or semi-empirical models and impacts replacement costs and LCOE.

3. Optimization Frameworks for Sizing and Control

Controls Co-Design

Simultaneous optimization of HESS component sizing and the associated control algorithm/tuning parameter (e.g., the moving-average controller span $K_{\rm control}$) is required to achieve minimal levelized cost of energy (LCOE). This was demonstrated in the co-design of tidal/PV microgrids with LIB and VRFB storage, where $K_{\rm control}$ is selected to best partition the power deficit between VRFB (long-term) and LIB (fast, high-rate) (Cohen et al., 2021).

Multi-Objective Optimization

Bi-level and multi-layer frameworks (e.g., NSGA-II for genetic optimization + fuzzy logic for control; decomposition into sizing and power split subproblems) enable simultaneous tradeoffs among CapEx, battery cycle life, vehicle/microgrid efficiency, and total cost of ownership (Yu et al., 2018, Andriesse et al., 29 Aug 2024, Bertucci et al., 2 Jun 2025).

Stochastic and Reinforcement Learning Approaches

• Deep RL (PPO, MADDPG): applied for real-time, uncertainty-aware HESS planning and operation in smart grids or renewable-heavy microgrids, directly learning operational policies for systems with battery and hydrogen storage to maximize profit, carbon reduction, and reliability (Kang et al., 2022, Samende et al., 2022).
• Predictive optimization with electro-thermal constraints: Nonlinear programming (NLP) incorporating battery temperature dependencies, HVAC, and curtailment to maximize net energy/revenue while staying within thermal operational bounds (Mishra et al., 2023).

4. Sizing Results, Application Case Studies, and Economic Analysis

Microgrid and Islanded Systems

In a tidal/PV microgrid case, the LCOE-minimizing configuration was $P_{\rm tidal}=1.7$ MW, $P_{\rm PV}=0.5$ MW, $K_{\rm control}=15$ h, with a LIB sized at 3 MWh/1 MW ($E/P \approx 3$ h, lifetime 7.9 yr) and a VRFB at 225 MWh/0.8 MW ($E/P \approx 280$ h, lifetime 15 yr). The calculated LCOE was \$1,186/MWh, where VRFB capex dominated (Cohen et al., 2021). Sensitivity analysis showed abrupt system architecture shifts when cost ratios between VRFB and LIB crossed critical thresholds.

Electric Vehicles

Multi-layer optimization with two-chemistry battery HESS (NCA–NMC) for a 60 kWh EV pack gives lowest energy consumption (11.62 kWh per standard drive cycle), with a 38.4/21.6 kWh split between NCA and NMC. Hybridization yields 1–2% savings over single chemistry and optimal balancing between mass, power-train efficiency, and thermal limits (Andriesse et al., 29 Aug 2024, Yu et al., 2018).

Smart Energy Networks and Grids

Integrated microgrids for truck charging and smart energy networks benefit from HESS architectures by reducing OpEx and grid dependency: fully hybrid (LIB+SC+FESS) systems achieved a 1.96% total cost reduction vs. battery-only schemes, with only a 2.6% increase in CapEx (Bertucci et al., 2 Jun 2025). For grid-interactive smart energy networks, multi-agent DRL controllers improved cost savings by 23.5% and reduced carbon emissions by 78.7% compared to baseline models (Samende et al., 2022).

Hydrogen Storage and Sector Coupling

In large-scale offshore wind platforms, parallel BESS and HESS provide resilience for zero-CO$_2$ operation; optimal designs dictated by the required wind-off backup time, with HESS contributing to total system cost in direct proportion to the resilience duration. Levelized costs $100–120$/MWh are achievable, and joint optimization with BESS can further reduce these figures (Zhao et al., 2022).

5. Energy Management, Control, and Real-Time Implementation

Filtered and Rule-Based Power Splitting

Savitzky–Golay filters, moving-average low-pass controllers, and fuzzy logic are intensively used to partition power flows between rapid-response and long-duration storage. Hierarchical decomposition (e.g., frequency-domain separation of load) assigns high-frequency power to SC/FESS and low-frequency to battery/VRFB, reducing battery stress and loss (Lin, 2020, Cohen et al., 2021).

Fuzzy Logic and Autoregressive Deep Learning

Fuzzy logic controllers (Mamdani-type) are widely adopted for real-time weighting of device contributions—input variables may include SOC/SOE, forecasted load, device temperature/state, and grid price. For SOC estimation in HESS (EV applications), data-driven NARX neural networks attained sub-0.1% error, outperforming UKF and classic ANN models and reducing computational cost, crucial for embedded deployment (Udeogu, 2022).

Model-Predictive and Comfort-Oriented Building Control

For residential sector HESS (PV+BESS+H$_2$/FC), fuzzy logic-based and MPC comfort-oriented energy management systems (ComEMS4Build) preserve occupant thermal comfort and optimize HESS utilization, achieving near-optimal economic performance relative to forecast-driven MPC and outperforming traditional rule-based controllers in both cost and comfort metrics (Kovačević et al., 6 Nov 2025).

6. Sizing, Design, and Deployment Guidelines

Best-practices for HESS deployment in microgrids and vehicle applications include:

• Size each storage sub-system explicitly based on the load/generation timescale decomposition and corresponding capital and operational cost models (nonlinear for flow batteries, electro-thermal for LIB).
• Integrate cycle-life and premature failure models in early design studies: neglecting these effects substantially underestimates LCOE and lifecycle cost.
• Employ co-design methodologies (simultaneous sizing and control tuning) over sequential design for system-level optimality.
• Use two-stage optimization (coarse grid search for convexity analysis, then swarm/global or MILP solution) to achieve robust results with high computational efficiency.
• For high-renewable or fast-charging regimes, include supercapacitors or flywheels to buffer the battery, enhancing both system reliability and battery lifetime.
• Systematically evaluate technology–cost sensitivities: architecture and economic optimum may change abruptly when key technology costs cross critical thresholds.

7. Future Directions, Limitations, and Research Opportunities

Challenges include integrating more sophisticated health estimation (state-of-health, temperature-cycled degradation) into real-time HESS control, modeling and controlling across wider timescales (seasonal, daily, milliseconds), and designing hybridization-aware cost incentives for future networked and sector-coupled energy systems. Advances in DRL, hierarchical model-predictive control, and data-driven system identification are rapidly enhancing the adaptability and robustness of HESS deployments in uncertain, high-renewable operational contexts (Kang et al., 2022, Andriesse et al., 29 Aug 2024). A plausible implication is that as new storage chemistries mature, and as energy management strategies become more adaptive, HESS will become the default architecture for both stand-alone and grid-supporting energy systems.